Section I Surveying Measurements Leveling, horizontal and slope distance, angles and directions 2. Angles and Directions Angles and Directions الزوایا و الاتجھات
Angles and Directions 1- Angles: Horizontal and Vertical Angles Horizontal Angle: The angle between the projections of the line of sight on a horizontal plane. Vertical Angle: The angle between the line of sight and a horizontal plane. 2- Directions: Direction of a line is the horizontal angle between the line and an arbitrary chosen reference line called a meridian. We will use north or south as a meridian Distinguish between angles, directions, and readings. الانحراف Angles and Azimuth Azimuth: Horizontal angle measured clockwise from a meridian (north) to the line, at the beginning of the line -The line A starts at A, the line A starts at.
Azimuth and earing الانحراف و الانحراف المختصر earing (reduced azimuth): : acute حادة horizontal angle, less than 90, measured from the north or the south direction to the line. Quadrant is shown by the letter or S before and the letter E or W after the angle. For example: 30W is in the fourth quad الرابع. الربع Azimuth and bearing: which quadrant ربع اى? 4 th QUAD. AZ = 360 - AZ = 1 ST QUAD. E 3 rd QUAD. AZ = 180 + AZ = 180-2 nd QUAD.
Departures and Latitudes المركبات السینیة و الصادیة ΔΧ ΔΥ ΔE Δ L* L* sin(az) cos(az Azimuth Equations How to know which quadrant from the signs of departure and latitude? For example, what is the azimuth if the departure was (- 20 m) and the latitude was (+20 m)? The following are important equations to memorize and understand tan(az A) = E E E A A Departure Latitude E L * sin( L * cos( AZ ) AZ ) E = E A + E A = A + A Azimuth C = Azimuth A +?
AZ C = AZ A + 180 + C AZ A 180 AZ A AZ C A AZ C = AZ A + 180 - AZ C AZ A 180 AZ A A C
C انحراف خط = انحراف الخط قبلھ + 180 ± الزاویھ الداخلھ A A C Azimuth of a line such as C = Azimuth of A ± The angle +180 Sign is + if the polygon is to the right clockwise : angles measured clockwise, letters are in a counterclockwise sequence. Easting and orthing P (E,) α L In many parts of the world, a slightly different form of notation is used. instead of (x,y) we use E, (Easting, orthing). In Egypt, the Easting comes first, for example: (100, 200) means that easting is 100 In the US, orthing might be mentioned first. It is a good practice to check internationally produced coordinate files before using them. E
Polar Coordinates +P (r, u ) r u E -The polar coordinate system describes a point by (angle, distance) instead of (X, Y) -We do not directly measure (X, Y in the field -In the field, we measure some form of polar coordinates: angle and distance to each point, then convert them to (X, Y) Examples
Example (1) Calculate the reduced azimuth of the lines A and AC, then calculate the reduced azimuth (bearing) of the lines AD and AE Line Azimuth A 120 40 AC 310 30 AD S 85 10 W A E 85 10 W Reduced Azimuth (bearing) Example (1)-Answer Line Azimuth Reduced Azimuth (bearing) A 120 40 S 59 20 E AC 310 30 49 30 W AD 256 10 S 85 10 W A E 274 50 85 10 W
Example (2) Compute the azimuth of the line : - A if Ea = 520m, a = 250m, Eb = 630m, and b = 420m - AC if Ec = 720m, c = 130m - AD if Ed = 400m, d = 100m - AE if Ee = 320m, e = 370m ote: The angle computed using a calculator is the reduced azimuth (bearing), from 0 to 90, from north or south, clock or anti-clockwise directions. You Must convert it to the azimuth α, from 0 to 360, measured clockwise from orth. Assume that the azimuth of the line A is (α A ), the bearing is = tan -1 (ΔE/ Δ) If we neglect the sign of as given by the calculator, then, 1st Quadrant : α A =, 2nd Quadrant: α A = 180, 3rd Quadrant: α A = 180 +, 4th Quadrant: α A = 360 -
- For the line (ab): calculate ΔE ab = E b E a and Δ ab = b a - If both Δ E, Δ are - ve, (3rd Quadrant) α ab = 180 + 30= 210 - If bearing from calculator is 30 & Δ E is ve& Δ is +ve α ab = 360-30 = 330 (4th Quadrant) - If bearing from calculator is 30& ΔE is + ve& Δ is ve, α ab = 180-30 = 150 (2nd Quadrant) - If bearing from calculator is 30, you have to notice if both ΔE, Δ are + ve or ve, If both ΔE, Δ are + ve, (1st Quadrant) α ab = 30 otherwise, if both ΔE, Δ are ve, (3 rd Quad.) α ab = 180 + 30 = 210 Example (2)-Answer Line ΔE Δ Quad. Calculated bearing tan-1( 1(ΔE/ Δ) Azimuth A 110 170 1st 32 54 19 32 54 19 AC 200-120 2nd -59 02 11 120 57 50 AD -120-150 3rd 38 39 35 218 39 35 AE -200 120 4th -59 02 11 300 57 50
Example (3) The coordinates of points A,, and C in meters are (120.10, 112.32), (214.12, 180.45), and (144.42, 82.17) respectively. Calculate: a) The departure and the latitude of the lines A and C b) The azimuth of the lines A and C. c) The internal angle AC d) The line AD is in the same direction as the line A, but 20m longer. Use the azimuth equations to compute the departure and latitude of the line AD. Example (3) Answer a) Dep A = ΔE A = 94.02, Lat A = Δ A = 68.13m Dep C = ΔE C = -69.70, Lat C = Δ C = -98.28m b) Az A = tan-1 (ΔE/ Δ) = 54 04 18 Az C = tan-1 (ΔE/ Δ) = 215 20 39 c) clockwise : Azimuth of C = Azimuth of A - The angle +180 Angle AC = AZ A - AZ C + 180 = = 54 04 18-215 20 39 +180 = 18 43 22 A C
d) AZ AD : The line AD will have the same direction (AZIMUTH) as A = 54 04 18 LAD = (94.02)2 + (68.13)2 = 116.11m Calculate departure = ΔE = L sin (AZ) = 94.02m latitude = Δ= L cos (AZ)= 68.13m Example (4) E A 115 105 120 90 30 110 D In the right polygon ACDEA, if the azimuth of the side CD = 30 and the internal angles are as shown in the figure, compute the azimuth of all the sides and check your answer. C
Example (4) - Answer E A 115 105 CHECK : earing of CD = earing of C + Angle C + 180 D 30 = 120 + 90 + 180 = 120 30 (subtracted from 360), O. K. 90 110 earing of DE = earing of CD + Angle D + 180 = 30 + 110 + 180 = 320 earing of EA = earing of DE + Angle E + 180 = 320 + 105 + 180 = 245 (subtracted from 360) earing of A = earing of EA + Angle A + 180 = 245 + 115 + 180 = 180 (subtracted from 360) earing of C = earing of A + Angle + 180 =180 + 120 + 180 = 120 (subtracted from 360) C Instruments Regular and Digital Theodolites Regular Theodolites: theologies measure the horizontal and vertical angles by measuring the amount of rotation around a horizontal and a vertical axes on graded circles
Gurley Antique Thodolite Digital Theodolites Can read and record horizontal and vertical angles in digital format
Total Stations Measure angles and distances and performs computations A total station includes a digital thodolite for angles, an EDM for distances, and a processor for computations.
Prism and sighting target Pole and tripod Aiming at a prism through the telescope of a total station in a zoo!
Multi Prisms, or group for a longer distance
Total station Vs EDM. Data collectors. Prismless total stations Robotic and Prismless Total Stations Methodology Advantages